Problem: Stephanie is 28 years younger than Vanessa. Vanessa and Stephanie first met 3 years ago. Twenty years ago, Vanessa was 5 times as old as Stephanie. How old is Vanessa now?
Answer: We can use the given information to write down two equations that describe the ages of Vanessa and Stephanie. Let Vanessa's current age be $v$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $v = s + 28$ Twenty years ago, Vanessa was $v - 20$ years old, and Stephanie was $s - 20$ years old. The information in the second sentence can be expressed in the following equation: $v - 20 = 5(s - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = v - 28$ . Substituting this into our second equation, we get the equation: $v - 20 = 5($ $(v - 28)$ $ -$ $ 20)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 20 = 5v - 240$ Solving for $v$ , we get: $4 v = 220$ $v = 55$.